Before doing an engine flush I would be doing a baseline compression test. Then you can try to do an engine flush. My "Go To" for engine flushing are Seafoam in the crankcase, and separately running ATF in the engine for 20 minutes or so at fast idle (under 2,000 RPM). I would not put any kind of load on the engine during the flush with Seafoam or ATF. Once the flushing is done, put in fresh oil and a new quality oil filter. I am assuming you are running with a conventional flat tappet valvetrain. If so, you need to select an engine oil that has Zinc in it, otherwise you can end up with a cam with flat lobes and/or lifters that have has their crown face surface worn away - and very quickly at that. New engine pils do not have Zinc any longer, as it fouls catalytic converters. Newer engines now use Roller Lifters in the valvetrains, so Zinc is no longer needed.
The oil I prefer to use is AmsOil Z-Rod 10W-30. It is a full synthetic, has a lor of detergent plenty of Zinc to protect your camshaft and lifters. If your compression test indicated your compression is consistently lower than expected for all cylinders it is an indication your compressions rings and cylinder walls have become worn. To help keep the engine from slurping down the AmsOil 10W-30 you can move to their 10W-40 (or heavier) Z-Rod oil), I prefer to not move to a thicker, higher viscosity oil unless the oil I am using is being consumed too quickly.
Once you have fresh oil in the engine, and new filter (I like Motorcraft FL-1A, or a Wix Premium, or NAPA Gold or Platinum filter), you ought to do another compression test to see if the compression has improved with the cleaner engine interior. With luck the engine flush(es) helped free any sticking rings up, and increased your compression. If the heavy smoking on heavy acceleration continues, especially if the compression has not increased by much, as another respondent (cjstaci) said above, you will know what to do.
If the worst befalls you, and you need to rebuild the engine due to worn compression and oil control rings, I have some suggestions (of course). First, do not go cheap. Invest once, do not buy twice. Have hardened steel seats installed for all the exhaust valve seats in the heads. Have the valve guides Bronze Walled for longevity. Instead of using oem-like oil seals (upside down umbrella oil deflectors at best), have your machine shop install Perfect Circle valve guide seals. They will help control oil consumption far longer than the oem excuse for an oil seal. Use a double roller all metal timing chain and gear set, avoid using any gears with a nylon or plastic tipping. The nylon/plastic tipped gears are quieter than all steel, but in time they begin to fleck off, loosening your chain more than necessary with an older engine. When you select pistons get a nice set of high performance (not racing) forged aluminum alloy pistons, but resist the temptation to go to a compression ration higher than 9.5:1, otherwise you will be fighting preignition, maybe even have to retard ignition timing to prevent excess pinging or preignition related detonation. A Hydraulic Roller Cam and lifter kit is costly, but it will provide you with a longer running engine that will be able to rev very nicely without valve float. If you want to get a larger carburetor (larger than 650 CFM) I recommend you get a carburetor with Vacuum Secondaries as by design the secondaries will only begin to open then the engine is really capable of using higher flow levels - otherwise you could end over carbing the engine, especially at low to middle RPM levels.
As much fun as a rebuilt engine can be when done correctly, I do hope the engine flushing and fresh oil helps remedy your excessive blowby issue.
